The theory of geminate and bimolecular diffusion influenced reactions was used to interpret the rebinding of carbon monoxide to protoheme following photodissociation measured over ten decades of time (1ps to 10ms). It was shown that the highly nonexponential behavior of the initial geminate phase, which cannot be explained using simple kinetic schemes, is a reflection of the diffusive motion of the reactants. Molecular dynamics simulations have been used to obtain the kinetics of a simple model of fluorescence quenching in a hard sphere liquid. These computer generated "experimental" results we then used to test the Smoluchowski theory of irreversible reactions. Considering the many particle nature of the problem, the agreement between theory and simulations was surprisingly good over a wide range of quencher concentrations. The Smoluchowski theory has been generalized to treat second order reversible diffusion-influenced bimolecular reactions. It was shown that a small initial deviation of the concentrations from their equilibrium values decays to zero nonexponentially in contrast to the prediction of ordinary chemical kinetics. A theory was developed to obtain the time dependent rate of binding of ligands to a cell partially covered by receptors. A special case of the result derived in this work was used to find an analytic expression for the current at a random array of microdisk electrodes. Finally, a new brownian dynamics algorithm was developed to simulate the time dependent bimolecular rate coefficient for reactions involving species with complex geometries that interact via an arbitrary potential.